Image reconstruction has become more and more important in the last few years especially in the field of medical imaging. Limited angle tomography is increasingly applied in interventional and diagnostic X-ray imaging. Examples are interventional C-arm systems using acquisitions at reduced angular range, mammography tomosynthesis or tomosynthesis for RAD applications. In addition, gating signals representing breathing or cardiac motion are used to reduce the angular range available for reconstruction. In case of limited angular range, iterative reconstruction is a very flexible reconstruction which can be applied. For example algebraic reconstruction techniques (ART), simultaneous algebraic reconstruction techniques (SART) or simultaneous iterative reconstruction technique (SIRT) may be mentioned. Prior knowledge to regularize the reconstruction can be included. One of the disadvantages of iterative reconstruction is its high computational effort and the inability to perform region of interest (ROI) reconstructions. For example US 2007/0053556 A1 and US 2007/0093711 A1 describe iterative data reconstruction methods.
As a technically different variant filtered back projection (FBP) is used in the art in order to reconstruct images. In the known FBP art the mathematically exact filters derived for complete data acquisition e.g. from computer tomography (CT) geometries are adapted for FBP when being applied to limited angle tomography. This may be based on individual impressions of reconstruction results in the reconstructed images. Such filters may be seen as heuristically generated filters. Thus, FBP methods use adapted filters which aim to reduce the effects of the insufficient projection acquisition and to generate image impressions which are advantageous for the clinical application target of the limited angle tomography. However, the filter derivation is not mathematically consistent and may therefore lead to image reconstruction results which are worse compared to the known iterative methods when applied to an incomplete data set.
Furthermore the known methods of filtered back projection (FBP) are not straight forward applicable to an incomplete projection data set like for example a limited angle tomography data set. For example a breast screening may only use an angular range of +/−10°, which results in an absolute angular range of 20°. This complicates image reconstruction.